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arXiv · 2607.03060

Concentration of mass of solutions to aggregation-diffusion equations

Grzegorz Karch·Krzysztof Krawczyk·Alexandre Boritchev
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Abstract

We consider the aggregation-diffusion equation in the whole space with a mildly singular interaction kernel K = K(x) which behaves like |x|^k near the origin for some k $\in$ (0, 2). This equation, supplemented with nonnegative, bounded, and integrable initial data, possesses a global-in-time solution. We prove that the family of nonnegative, radially symmetric solutions of this equation, all sharing the same initial datum, focuses around the origin over a common finite time interval as $\epsilon$ ___ 0.

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Grzegorz Karch, Krzysztof Krawczyk, Alexandre Boritchev. 2026-07-03. Concentration of mass of solutions to aggregation-diffusion equations. https://arxiv.org/abs/2607.03060

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